Nonlinear System Identification

The efficacy of the multimodel framework (MMF) in modeling and identification of complex, nonlinear, and uncertain systems has been widely recognized in the literature owing to its simplicity, transparency, and mathematical tractability, allowing the use of well-known modeling analysis and control design techniques. The approach proved to be effective in addressing some of the shortcomings of other modeling techniques such as those based on a single nonlinear autoregressive network with exogenous inputs model or neural networks. A great number of researchers have contributed to this active field. Due to the significant amount of contributions and the lack of a recent survey, the review of recent developments in this field is vital. In this two-part paper, we attempt to provide a comprehensive coverage of the multimodel approach for modeling and identification of complex systems. The study contains a classification of different methods, the challenges encountered, as well as recent applications of MMF in various fields. Part 1 of this paper presents an overview of MMF for modeling and identification of nonlinear systems as well as the review of recent developments in the partitioning strategies employed.

Teaching Aids for Modeling and Control of Hybrid Systems (CAMCHS)

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

Identification of nonlinear systems is one of the important problems in engineering. Chaotic systems are among those nonlinear systems that have been in the center of attention of many researchers because of their complex and unpredictable behaviors. This paper proposes an algorithm for optimally estimating the parameters of system by minimizing the mean of squared errors (MSE) index. In this paper, Teaching Learning Based Optimization (TLBO) algorithm is used for solving both offline and online parameter estimation problems for chaotic systems. The validity of this algorithm in terms of convergence speed and parameter accuracy in comparison to other popular optimization algorithms such as Standard PSO (PSO), Differential Evolution (DE), Adaptive Particle Swarm Optimization (APSO) and Genetic Algorithm (GA) is shown through an illustrative example for the modeling of chaotic systems. Furthermore, in order to demonstrate the feasibility of this algorithm, it is applied to the problem of parameter identification of a well-known nonlinear Lorenz chaotic system. According to simulation results, the proposed algorithm is a very suitable algorithm for online parameter identification for a class of nonlinear chaotic systems.

A new algorithm is presented for the identification of non-linear lumped time-invariant SISO systems. The method is based on differentiation properties of the exponential Fourier series and can be used to identify a wide class of systems. Identification of two specific systems is studied. An illustrative example is provided which shows that the algorithm gives accurate parameter estimates

Multidimensional membership functions in T–S fuzzy models for modelling and identification of nonlinear multivariable systems using genetic algorithms

Identification of nonlinear systems using NARMAX model

International audience

This article presents a theoretical framework for the identification of nonlinear dynamic MISO systems with orthonormal base function models on fundamental basics of the Volterra theory. In the past the Volterra theory was used for the identification of nonlinear dynamic SISO systems (e.g. Hammerstein and Wiener models). In principle it is possible to extend these approaches to systems with more than one input (i.e. MISO systems). In former times this failed due to a lack of computational performance. In this paper an approach is presented which allows the identification of arbitrary coupled Hammerstein and Wiener models with multiple inputs. Some fundamental considerations for the identification of MISO systems based on arbitrary coupled Hammerstein models are made and extended to MISO systems based on arbitrary coupled Wiener models. This extended Volterra theory results in equations where the unknown parameters can be separated of the input values in a linear manner. In order to approximate the truncated impulse responses of the linear dynamic systems and to reduce the number of unknown parameters orthonormal base functions (OBFs) are introduced. As an example the proposed identification method is applied to a MISO system based on forward and backward coupled Hammerstein and Wiener models.

Publication in the conference proceedings of EUSIPCO, Trieste, Italy, 1996

We propose a new perspective on the identification of linear dynamic system using structural similarity. The proposal consists in the meaningful exploration of each model, specifically behavior of the state variable. The decomposition of the behavior of a state variable in different modes of behavior of a system, each one has a different set of weights and shows different patterns of behavior. These weights are more significant than eigenvalue to develop a new technique for identifying linear system and invariants over time. We use two methods based on different areas of knowledge such as linear algebra and statistics. This paper is a conceptual proof that enriches the implementation and validity not only from point of view algorithmic likewise physic mathematical.

A globally consistent nonlinear least squares estimator for identification of nonlinear rational systems

The local linear modelling approach is capable of modelling complex nonlinear processes. The transparency of the model architecture permits the incorporation of prior knowledge in different ways and the integration of process knowledge and experimental data has been demonstrated in detail for the modelling of the heat exchanger. Utilising an arbitrary local modelling strategy does not automatically guarantee a transparent model. The employed LOLIMOT algorithm has proven to yield transparent and well interpretable models. The appropriate choice of an excitation signal is vital for a good model. Here, the transparency of the local structure again aids the engineer in the design and the assessment of the excitation signal. The interpretability of the local structure offers simple ways for the validation of the identified model based on local characteristic values as process gains or time constants. The obtained local linear models can further be utilised in model-based control approaches as well as process monitoring or fault detection.

Identification of nonlinear systems by use of nonstationary white-noise inputs

Nonlinear model identification of an experimental ball-and-tube system using a genetic programming approach